Tuesday 26 April 2011 16.10 EDT
First published on Tuesday 26 April 2011 16.10 EDT

He may have been one of the 20th century's greatest philosophers – perhaps the greatest – but Ludwig Wittgenstein could have been so many other things if he had turned his mind to it. An engineer, for example: he designed an aero engine in 1909. A mathematician, perhaps: he debated theory with one of his students, Alan Turing, before the latter cracked the Enigma code. Or, least likely, an international playboy: Wittgenstein inherited millions on the death of his multibillionaire father, Karl, a self-made Austrian steel magnate.

It is typical of Wittgenstein that he gave all the money away – much of it to penniless poets and artists. But this was a man who sat on the knee of Brahms as a child and whose brother Paul was a celebrated concert pianist both before and after losing an arm in the war. (Ravel wrote his Piano Concerto for the Left Hand for him.)

His relationship with Paul speaks volumes about Wittgenstein. One day Paul was practising as the overly critical Ludwig sat in the next room but just could not go on, bursting in on his brother and saying: "I cannot play when you are in the house as I feel your scepticism seeping towards me from under the door."

As professor of philosophy at Cambridge he antagonised most of his students by throwing them out of lectures for failing to lay into him or ask pertinent questions. At one stage there was just one left – Francis Skinner.

During his lifetime there was little formal publication of his philosophy apart from his early book the Tractatus Logico-Philosophicus, which he finished writing in the first world war trenches fighting for the Austrians.

He will, of course, be remembered as an enormously influential philosopher whose work challenged much past and contemporary thought.

Wittgenstein's central theories were around mathematics and science. He said we had to give up the idea that science and maths are machines which you can just switch on and then they work – yes, science is a language game, but it is much more arbitrary than we think.

Among his maxims are that we are "not here to enjoy ourselves," and: "Death is not an event in life: we do not live to experience death."